Integration: the Area Problem
Key Questions

Let us look at the definition of a definite integral below.
Definite Integral
#\int_a^b f(x) dx=lim_{n to infty}sum_{i=1}^n f(a+iDelta x)Delta x# ,
where#Delta x ={ba}/n# .If
#f(x)ge0# , then the definition essentially is the limit of the sum of the areas of approximating rectangles, so, by design, the definite integral represents the area of the region under the graph of#f(x)# above the xaxis. 
If we consider the general integral:
# I = int_a^b \ f(x) \ dx # Then the Integration calculates the "net" area between the curve
#y=f(x)# from#x=a# to#x=b# , and the#x# axis.
By "net" area, we consider any area below the curve and above the
#x# axis to be positive , and any area above the curve and below the#x# axis to be negative.
Questions
Introduction to Integration

Sigma Notation

Integration: the Area Problem

Formal Definition of the Definite Integral

Definite and indefinite integrals

Integrals of Polynomial functions

Determining Basic Rates of Change Using Integrals

Integrals of Trigonometric Functions

Integrals of Exponential Functions

Integrals of Rational Functions

The Fundamental Theorem of Calculus

Basic Properties of Definite Integrals